Hu Jun Edition, episode 38, kills Duan's woman. Does Duan Yanqing know that Duan Yu is his son after seeing Duan Yu's birthday book?

You mean the stupid version. In fact, Jin Yong has explained these problems in the revision of "Tian Long Ba Bu".

First of all, Duan Yanqing didn't know that Duan Yu was his son until he saw Duan Yu's eight characters, because he knew that she was Guanyin outside Tianlong Temple when he saw Dao Baifeng, and he knew that Duan Yu was not Duan's son but his when he saw Duan Yu's eight characters, so he saved Duan Yu at a critical moment.

Then, I want to kill Mrs. Wang. It should be said that I was induced by Duan. Duan looked at the woman he liked and indirectly died at the hands of Mrs. Wang, and decided to avenge them. Therefore, it doesn't matter that Mu Rongfu killed those women in front of Mu Rongfu. He only cares about Mrs. Wang; In order to force Duan to give way, when Duan said this, he naturally threatened to kill Mrs. Wang.

Finally, Duan changed his mind and asked to kill Mrs. Wang because Duan saw Mrs. Wang's sad appearance and remembered their previous events, so he forgave Mrs. Wang in his heart and changed his mind and asked to kill Mrs. Wang. His purpose is to make Mu Rongfu suspicious and let Mrs. Wang go.